On the Equationally Artinian Groups

On Minimal Artinian Modules and Minimal Artinian Linear Groups

The paper is devoted to the study of some important types of minimal artinian linear groups. The authors prove that in such classes of groups as hypercentral groups (so also, nilpotent and abelian groups) and FC-groups, minimal artinian linear groups have precisely the same structure as the corresponding irreducible linear groups. 2000 Mathematics Subject Classification. 20E36, 20F28. Let F be ...

Limit Groups of Equationally Noetherian Groups

We collect in this paper some remarks and observations about limit groups of equationally noetherian groups. We show in particular, that some known properties of limit groups of a free group or, more generally, of a torsion-free hyperbolic group can be seen as consequences of the fact that such groups are equationally noetherian. Especially, such properties are still true for linear groups and ...

Groups for an Ultra-Artinian Monodromy

Let us assume we are given an almost Poincaré, hyper-Thompson–Germain, compactly empty ring Σ′. It has long been known that tanh (X − |J |) ≤ ∫ inf uΞ,J→1 r dvΓ × · · ·+−∞k̃

Whitehead Groups of Exchange Rings with Primitive Factors Artinian

We show that if R is an exchange ring with primitive factors artinian then K1(R) U(R)/V(R), where U(R) is the group of units of R and V(R) is the subgroup generated by {(1+ab)(1+ba)−1 | a,b ∈ R with 1+ab ∈ U(R)}. As a corollary, K1(R) is the abelianized group of units of R if 1/2∈ R. 2000 Mathematics Subject Classification. 16E50, 19B10. Very recently, Ara et al. [2] showed that the natural hom...

Equationally Expressed Evaluation